System and method for estimating flow capacity of a reservoir

ABSTRACT

The disclosure relates to a computer implemented method and system for determining a flow geometry of a subsurface reservoir, as well as a method of hydrocarbon production with flooding. A general embodiment of the disclosure is a method for determining a flow geometry of a subsurface reservoir, the method comprising: (a) receiving production related data for the reservoir, wherein the reservoir is associated with a flooding operation; (b) generation a heterogeneity factor from the production related data; (c) calculating a flow geometry of displacement of hydrocarbons from the reservoir responsive to the heterogeneity factor; and (d) outputting the flow geometry.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority from U.S. Provisional Application No. 61/939590, filed on Feb. 13, 2014, Chevron Dkt. No. T-9397-P, the disclosure of which is hereby incorporated by reference in its entirety.

TECHNICAL FIELD

The present disclosure generally relates to a system and method for evaluating flow capacity of a reservoir given heterogeneity factors, and more particularly, to a system and method for using a heterogeneity factor to generate a flow geometry of a reservoir.

BACKGROUND

Reservoirs, such as petroleum reservoirs, typically contain fluids such as water and mixture of hydrocarbons such as oil and gas. To produce the hydrocarbons from the reservoir, different mechanisms can be utilized such as primary, secondary or tertiary recovery processes.

In a primary recovery process, hydrocarbons are displaced from a reservoir due to the high natural differential pressure between the reservoir and the bottomhole pressure within a wellbore. The reservoir's energy and natural forces drive the hydrocarbons contained in the reservoir into the production well and up to the surface. Artificial lift systems, such as sucker rod pumps, electrical submersible pumps or gas-lift systems, are often implemented in the primary production stage. However, even with use of such artificial lift systems only a small fraction of the original-oil-in place (OOIP) is typically recovered using primary recovery processes as the reservoir pressure, and the differential pressure between the reservoir and the wellbore intake, declines overtime.

In order to increase the production life of the reservoir, secondary or tertiary recovery processes can be used. Typically in these processes, fluids such as water, gas, surfactant, or combination thereof, are injected into the reservoir to maintain reservoir pressure and drive the hydrocarbons to producing wells. The most commonly used secondary recovery process is waterflooding, and involves the injection of water into the reservoir to displace or physically sweep the residual oil to adjacent production wells.

Reservoir heterogeneity (e.g., variation in a reservoir due to rock properties, naturally occurring fractures, etc.) is the leading cause of poor sweep efficiency and bypassed oil. This bypassed oil cannot be produced from the existing field without some kind of well intervention or infill drilling program. If signs of bypassed oil can be identified from existing production data, the best reservoir management practice (infill or intervention) can be selected.

Methods for estimating bypassed oil frequently rely on numerical reservoir models, which can be inaccurate. Other methods, such as capacitance resistance modeling (CRM; Sayarpour, 2008), use injection and production data to infer well connectivity, which may indirectly describe bypassed oil (quick response + unequal connectivity=poor sweep). If well productivity indices are known, CRM can directly estimate volume swept. The advantage of CRM is that it relies on observed field data alone, thereby restricting uncertainty and associated errors to measurement errors (i.e., model and reservoir uncertainties are not included). CRM can give a good idea of swept volume and connectivity, but not formation heterogeneity, and cannot necessarily determine the best reservoir management practice noted above.

Another production-derived method to identify bypassed oil was first developed for laboratory scale, miscible floods in the early 1960s (Koval, 1963). Koval's method has the advantage of simultaneously estimating pore volume being drained and field heterogeneity from the evolution of produced water cut at the well, sector, or sand scale. These two properties directly impact remaining (bypassed) oil, with large heterogeneity and small volume drained indicative of poor sweep efficiency. By contouring these properties on a reservoir map, one could visually locate promising infill opportunities.

However, more information about flooding and the reservoir undergoing flooding can be beneficial, and therefore, the industry continues to search for improvements related to flooding.

SUMMARY

The disclosure relates to a computer implemented method and system for determining a flow geometry of a subsurface reservoir. A general embodiment of the disclosure is a method for determining a flow geometry of a subsurface reservoir, the method comprising: (a) receiving production related data for the reservoir, wherein the reservoir is associated with a flooding operation; (b) generating a heterogeneity factor from the production related data; (c) calculating a flow geometry of displacement of hydrocarbons from the reservoir responsive to the heterogeneity factor; and (d) outputting the flow geometry.

The disclosure includes a system for determining a flow geometry of a subsurface reservoir. The system includes a processor and a memory storing computer executable instructions that when executed by the processor cause the processor to (a) receive production related data for the reservoir, wherein the reservoir is associated with a flooding operation, (b) generate a heterogeneity factor from the production related data, (c) calculate a flow geometry of displacement of hydrocarbons from the reservoir responsive to the heterogeneity factor, and (d) output the flow geometry.

The disclosure also includes a method for hydrocarbon production from a subterranean reservoir, comprising flooding the subsurface reservoir in accordance with a flow geometry generated by the method of claim 1.

The foregoing has outlined rather broadly the features and technical advantages of the present disclosure in order that the detailed description of the disclosure that follows may be better understood. Additional features and advantages of the disclosure will be described hereinafter. It should be appreciated by those skilled in the art that the conception and specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the scope of the disclosure as set forth in the appended claims. The novel features which are believed to be characteristic of the disclosure, both as to its organization and method of operation, together with further objects and advantages will be better understood from the following description when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure, reference is now made to the following description taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a flow chart of an embodiment of a computer implemented method of generating a flow geometry.

FIG. 2 is an example of flow geometry illustrated as a flow capacity vs. storage capacity curve (F-Φ curve).

FIG. 3 shows an example F-Φ curve with field data (triangle) taken from tracer analysis and estimated F-Φ (square) calculated using methods of the disclosure.

FIG. 4 is a graph showing water cut from a producing well against the calculated water cut from the Koval analysis.

FIG. 5 illustrates the relationship between the Koval coefficient and Lorenz coefficient. The Koval coefficient comes from analysis of water cut, but the flow geometry curves (F-Φ) uses the Lorenz coefficient. FIG. 5 is used as a link between the two.

FIG. 6 illustrates an embodiment of a computing system for generating flow geometry.

FIG. 7 illustrates an embodiment of a method for hydrocarbon production from a subterranean reservoir comprising flooding the subterranean reservoir in accordance with a flow geometry generated, for example, by the embodiment of FIG. 1.

DETAILED DESCRIPTION

As used herein, the terminology “flow capacity vs.. storage capacity curve” is simplified as “F-Φ curve”. Furthermore, the terminology “flow geometry” is used interchangeably with the terminology “flow capacity vs. storage capacity curve” and “F-Φ curve”. For example, the F-Φ curve indicates flow geometry of displacement of hydrocarbons from a reservoir, thus calculating the F-Φ curve can be the same as calculating flow geometry. Moreover, the flow geometry, in some cases, is graphically represented by the F-Φ curve, but those of ordinary skill in the art will appreciate that some embodiments do not require graphically plotting the F-Φ curve.

As used herein “heterogeneity factor” refers to a measure (usually statistical) of the degree on non-uniformity of a permeable medium. for example, the Dykstra-Parsons coefficient is related to the variance of a log-normal distribution of permeability. In certain embodiments the heterogeneity factor is a Koval factor, a Lorenz coefficient, or Dykstra-Parsons coefficient.

As used herein “dynamic heterogeneity” refers to the interaction between the heterogeneous medium and the fluid displacement. This “dynamic” heterogeneity may be larger or smaller than the static heterogeneity. In certain embodiments the dynamic heterogeneity is represented by a F- the Koval factor or Lorenz coefficient.

The disclosure relates to a computer implemented method and system for determining a flow geometry of a subsurface reservoir. A general embodiment of the disclosure is a method for determining a flow geometry of a subsurface reservoir, the method comprising: (a) receiving production related data for the reservoir, wherein the reservoir is associated with a flooding operation; (b) generating a heterogeneity factor from the production related data; (c) calculating a flow geometry of displacement of hydrocarbons from the reservoir responsive to the heterogeneity factor; and (d) outputting the flow geometry. In embodiments, the heterogeneity factor is at least one of a Koval factor, a Lorenz coefficient, or a Dykstra-Parsons coefficient. The production related data is at least one of production rate of water, water cut, production rate of oil, production rate of gas, injection pressure, injection volume, temperature, natural tracers, artificial tracers, or tracer proxies.

In some embodiments, the heterogeneity factor is the Koval factor, and the Koval factor is generated from the production related data (e.g., by minimizing the misfit between field data and model data.) More specifically, the Koval factor is generated from the production related data that includes water cut data. Calculating the flow geometry can include converting the Koval factor to a Lorenz coefficient. Calculating the flow geometry can further comprise minimizing an objective function, and minimizing the objective function comprises minimizing a difference between a field Lorenz coefficient and a modeled Lorenz coefficient

$F = ^{\frac{1}{\alpha}{\lbrack{{\ln \; \Phi} + \frac{({1 - \Phi})}{\beta}}\rbrack}}$

and in some cases Φ is less than 0.5. In some embodiments, data points in the production data are weighted based on perceived error. In specific embodiments, discrepancies in the production related data are removed from the production related data set used in the calculation.

Thus, calculating the flow geometry from the Koval factor can comprise calculating a Lorenz coefficient from the Koval factor, and in some examples, a F-Φ curve is generated from the Lorenz coefficient. The method can further comprise optimizing operating parameters from the flow geometry, locating potential infill opportunities based at least in part on the flow geometry, optimizing sweep based at least in part on the flow geometry, and/or optimizing size of conformation treatments based at least in part on the flow geometry. The flow geometry can be graphically displayed in a F-Φ curve.

Some embodiments include estimating flow geometry (F- ) based on known production data. This process includes applying an equation for estimating heterogeneity, such as a Koval factor, Lorenz coefficient, or Dykstra-Parsons coefficient (and in some embodiments, matching the heterogeneity factor with a parametric expression for the dynamic heterogeneity subject to constraints). The flow geometry, in some cases, is graphically represented by a F-Φ curve. Specific embodiments include estimating pore volume drained and a Koval factor (which describes heterogeneity) by minimizing an objective function. The objective function describes the misfit between observed water cut and the water cut derived from Koval's equation.

By generating the flow geometry, the flow paths of the subsurface reservoir may be potentially replicated to get a better idea of the flooding. Moreover, qualitative information and/or quantitative information may be generated based on the flow geometry. The following information may be generated: qualitative information such as x percentage of flow from y percentage of pore volume of the reservoir and quantitative information such as slug size for conformance control and estimate of sweep vs time for the reservoir. As an example, if the computing system determines that 90% of flow is coming from 10% of pore volume of the reservoir, then an engineer or other decisionmaker can decide on a different course of action for the flooding of the reservoir to try to displace hydrocarbons from the other 90% of pore volume of the reservoir that is not being swept by the flooding operation. Aspects of the present disclosure can be utilized for determining the best (or a better) method to optimize sweep efficiency in a subsurface reservoir from production data.

FIG. 1 describes an embodiment of the flow geometry generating method that is computer implemented (100). First, production related data is received or collected (105). For example, at 105, production related data can be received for a reservoir, where the reservoir is associated with a flooding operation (e.g., receive water cut data for a reservoir undergoing waterflooding is received). The production related data can include dates of collection, uptime, oil collected (bbl), gas collected (scf), water collected (bbl), cumulative oil, cumulative gas, cumulative water, and total liquid (bbl), for example. User supplied input for directing the calculations can also be received and this data can include PVT parameters.

The production related data may optionally be weighted to remove any outlying data points (110). An example weighing calculation is shown in Example 1, below.

A heterogeneity factor can be generated from the production relate data (115) for example, a Koval factor can be generated from the water cut data, as illustrated in FIG. 4. In some embodiment, a Koval factor is generated from the production data by minimizing an objective function.

A flow geometry of displacement of hydrocarbons from the reservoir can be calculated responsive to the heterogeneity factor (120), as illustrated in FIG. 2. For example, at 120, the F-Φ curve can be calculated responsive to the Koval Factor (i) converting the Koval Factor to a Lorenz coefficient (Lc), as illustrated in FIG. 5, and (ii) minimizing an objective function comprising minimizing a difference between a field Lorenz coefficient and a modeled Lorenz coefficient

$F = ^{\frac{1}{\alpha}{\lbrack{{\ln \; \Phi} + \frac{({1 - \Phi})}{\beta}}\rbrack}}$

and in some cases Φ is less than 0.5.

Optionally, if tracer data is available, the flow geometry is calculated responsive to the tracer data (125). For example, the tracer data can optionally constrain the flow geometry that is calculated at 125. Tracer data may be available for a portion of the subsurface reservoir, but the entire subsurface reservoir. Thus, the available tracer data can be used to constrain the flow geometry that is generated so that the flow geometry is consistent or conforms to the available tracer data. Alternatively, or additionally, the tracer data can be utilized to check the accuracy of the flow geometry. This item is optional and tracer data is not necessary for the other items in FIG. 1.

The generated flow geometry can be output (130) and/or used for other purposes. For example, the generated flow geometry can be used to optimize sweep based at least in part on the flow geometry (135), optimize size conformance treatment based at least in part on the flow geometry (140), optimize operating parameters based at least in part on the flow geometry (145), and/or locate at least one potential infill opportunity based at least in part on the flow geometry (150). Each step is described in more detail below and example calculations are given in Example 1.

FIG. 7 provides an embodiment of a method of hydrocarbon production with flooding. For example, flooding material (e.g., water, surfactant, etc.) can be injected into an injection well of a subsurface reservoir to displace and sweep hydrocarbons of the subsurface reservoir to a production well of the subsurface reservoir (705). At least a portion of the hydrocarbons of the subsurface reservoir can be produced via the production well of the subsurface reservoir 710. Based on production related data from the produced hydrocarbons (and fluid including the hydrocarbons), the computer implemented method described herein, for example, can be used to generate the flow geometry for the subsurface reservoir. Flooding of the subsurface reservoir can be performed in accordance with the flow geometry generated by the computer implemented method (715). For example, an operating parameter of a waterflooding can be adjusted, removed, or added. Additionally, or alternatively, infilling and other intervention or techniques like conformance control can be utilized. The produced fluid that includes the hydrocarbons can be recycled and reinjected into the same or different injection well and the flooding can continue (as illustrate in the loop of FIG. 7.

The Koval factor is one of three measures of heterogeneity in general use, the others being the Dykstra-Parsons (V_(DP)) coefficient and the Lorenz coefficient (L_(c)), all of which can be derived from one another. The Lorenz coefficient can be calculated directly from the F- (an example F- and is defined in terms of the divergence of the F- rca in FIG. 2). Therefore, in embodiments the fundamental statistic of the F-Φ curve can be given by the Koval analysis of water cut data.

Here a parametric form of F, F=f(Φ), was identified that mimics reservoir F-Φ characteristics. The slop of the F-Φ (Wu et al., 2008, incorporated herein by reference). Porous media exhibit the following characteristics in regards to residence time distributions;

1. There are a number of “fast paths” relative to the average, rather than “average and some slow paths.” That is, the slope of the curve is large relative to the mean at low values of Φ.

2. The mean (the point at which the slope is one, so describing the bulk flow) is not beyond Φ=0.5. That is, there are more flow paths slower than the mean than faster. Another way of stating this is that thief zones (faster velocity than the mean) occupy a smaller fraction of the formation.

As an example, the equation used to generate F(Φ) can be a 2-parameter equation:

$\begin{matrix} {F = ^{\frac{1}{\alpha}{\lbrack{{\ln \; \Phi} + \frac{({1 - \Phi})}{\beta}}\rbrack}}} & \left( {{Eq}.\mspace{14mu} 1} \right) \end{matrix}$

w-Φ curve can be generated by adjusting the match parameters. Another way to view this: any Lorenz coefficient can be generated by changing the match parameters. Thus, an example method comprises:

-   -   a) Generate a Koval factor from production data and convert         Koval to a Lorenz coefficient     -   b) arbitrary values, and construct a set of Φ (from 0 to 1, by         0.01 for example): Calculate F from the equation above.     -   c) Calculate Lc from the hypothetical (or model) F-Φ data.     -   d) Create an objective function that is (Field Lc-Modeled Lc)².         A direct solver (such as spreadsheet solver) is used to minimize         the objective function by Φ(slope=1) is between (e.g., 0.3 and         0.45). The lower limit is a strong function f the value of Lc.

This method has been tested on tracer-derived F-Φ data. The tracer data directly gave the F-Φ curve and Lc (method described in Shook et al., 2009). The value for Lc was entered and the process described above was engaged. The F and Φ data were then ‘binned’ into 20 bins (each an increment of 0.05 in Φ for example). FIG. 3 shows the comparison between the real F-Φ data (which the above method did not use) and the estimates derived only from the correct Lc value. Six blind tests have been done to date with similar accuracy.

Although references are made to extracting dynamic heterogeneity (that is, the apparent heterogeneity that arises from displacement) by using the Koval theory, any method that can provide an estimate of the Dykstra-Parsons coefficient or Lorenz coefficient can be used in the present method. A static measure of heterogeneity may be used, although sometimes there is poor correlation between dynamic heterogeneity and its static counterpart. While on such method is described below, the method is not restricted to such an embodiment. The disclosure is not to solely quantify the fundamental measure of heterogeneity (e.g., Lc), it is to describe the whole distribution of the flow field from that statistic.

Koval's Method

Embodiments of the disclosure use a heterogeneity factor to find a dynamic heterogeneity (or flow geometry). In certain embodiments, the heterogeneity factor is a Koval factor, as described further here. Koval theory (Koval, 1963) was originally proposed for unstable miscible displacements; however, if the flow is segregated, the theory can be applied to immiscible displacements as well. The key equation from Koval (1963) is given as

$\begin{matrix} {f_{w} = \frac{H_{K} - \sqrt{\frac{H_{K}}{t_{D}}}}{H_{K} - 1}} & \left( {{Eq}.\mspace{14mu} 2} \right) \end{matrix}$

The Koval factor, H_(k) includes an effective mobility ratio, E, and measure of the heterogeneity of the formation, H. The effective mobility ratio uses the quarter power mixing rule.

$\begin{matrix} {H_{K} = {HE}} & \left( {{Eq}.\mspace{14mu} 3} \right) \\ {E = \left\lbrack {0.78 + {0.22\left( \frac{\mu_{o}}{\mu_{w}} \right)^{1/4}}} \right\rbrack^{4}} & \left( {{Eq}.\mspace{14mu} 4} \right) \end{matrix}$

The volume swept by injected water is embedded in dimensionless time, t_(o). Koval (and conventional reservoir engineering) takes dimensionless time in ‘pore volumes injected.’ This would require knowledge of injection allocation among producers—another source of error. However, it is perfectly valid to consider dimensionless time in ‘pore volumes produces’ and ‘volume drained’ rather than swept.

$\begin{matrix} {t_{D} = \frac{\int_{0}^{t}{q_{p}\ {\tau}}}{V_{P}}} & \left( {{Eq}.\mspace{14mu} 5} \right) \end{matrix}$

where q_(p) is reservoir volumetric liquid production rate, and V_(p) is the pore volume drained by the producer. By recording production rates and phase cuts at the producer or sector level, both H_(k) and t_(o) (and therefore V_(p)) can be estimated using multivariate, non-linear regression (the more data, the better the regression).

As shown, the Koval factor can be computed as a product of dynamic heterogeneity and an effective mobility ratio. If oil viscosity changes spatially (e.g., due to biodegradation), the effective mobility ratio can be removed from H_(k) prior to contouring: if viscosity is relatively constant, there is no need to do so.

Use in the Field

F-Φ curves are 3-D, dynamic flow capacity—storage capacity diagrams, and have wide application in reservoir engineering and geology. Developed in the 1950's for simple conceptual studies, they were calculated from static properties of permeability, porosity, and layer thickness, and were referred to as F-C curves. They were generalized to 3-D, heterogeneous media by Shook and Mitchell (2009) and have been used to assess heterogeneity in Earth models (U.S. Pat. No. 8,428,924), catalog model heterogeneity as a function of depositional environment (U.S. Patent Publication No. 2013/0132052), and size conformance treatments (U.S. Patent Publication No. 2011/0320128), incorporated herein by reference. A key problem that this disclosure addresses is F-Φ curves could only be calculated from a model, or from tracer tests. Models are known to be only approximations to reality, and tracer testing is frequently time consuming and costly. The current disclosure obtains the F-Φ curve from production data alone.

EXAMPLES

The following examples are included to demonstrate specific embodiments of the disclosure. It should be appreciated by the those of skill in the art that the techniques disclosed in the examples that follow represent techniques discovered by the inventors to function well in the practice of the disclosure, and thus, can be considered to constitute modes for its practice. However, those skilled in the art should, in light of the present disclosure, appreciate that many changes can be made in the specific embodiments disclosed and still obtain a like or similar result without departing from the scope of the disclosure.

Example 1

This example was implemented in a spreadsheet which included production related data and user input for directing the calculations. The production related data included dates of collection (collected in daily increments), the name of the well, uptime, oil produced (bbl), gas produced (scf), water produced (bbl), cumulative oil, cumulative gas, cumulative water, liquid (bbl), and the calculated water cut (fw).

Because rates fluctuate daily the calculations were based on cumulative production of fluids. The data can be at any frequency: however, in this example was collected daily. Units were at surface conditions (STB for liquids, SCF for gas). PVT properties for water (Bw), oil (Bo), and gas (Bg and Rs) were also entered by the user.

Monthly production rate of oil (cumulative produced at date—cumulative produced the previous date) was calculated, as was the monthly production of water. These were then used to calculate water cut, which is the water cut to which the Koval method was matched to. However, because water cut can be noisy and not monotonically increasing (as assumed by Koval), a weight was assigned to the field water cuts. That weighting factor is described below in the calculation of the objective function.

Monthly production rate was changed to reservoir conditions using the standard conversion:

$\begin{matrix} {Q = \frac{{Q_{w}B_{w}} + {Q_{o}B_{o}} + {\left( {Q_{g} - {R_{S}Q_{o}}} \right) \cdot {B_{g}/5.615}}}{10^{6}}} & \left( {{Eq}.\mspace{14mu} 6} \right) \end{matrix}$

Note that volume produced has units of MMrb; the pore volume estimated from solving Eq. 2 will also be in MMrb.

The estimate of dimensionless time (Eq. 5 above) for an estimated pore volume was used as discussed below, as was the Koval model water cut (fw_(Kov)) calculated from Eq. 2 for an estimated pore volume and Koval factor. The weighted error between the field-observed water cut and the Koval prediction was also calculated.

Estimates for pore volume and Koval factor were used in the calculation of t_(D) and fw_(Kov) with the objective function as the weighted sum of the errors:

ObjFun=Σ[ω(fw-fw_(Kov))²]  (Eq. 7)

were fw is the observed water cut and fw_(Kov) is the (iterative) solution to Eq. 2. The weighting function, ω, is either zero or one:

ω=1 if fw >all previous “valid” fw (Koval's method required monotonically increasing fw), and

fw_(i)fw_(i-1) <0.2 (to avoid spurious large oscillations), and

fw >0.001 (to avoid weighting the regression with excessive zero water cuts)

ω=0 otherwise.

A water cut was considered “valid” if its weight is 1; this is meant to avoid including fw that failed the tests above, and thus were not included in the objective function calculations.

The solver is then activated to set the objective function to zero (or to as small a value as possible, e.g., 0.0001) by changing H_(k) and V_(p) from eqs. 2 and 5, and subjected to certain (field-specific) constraints for this example.

1. Volume drained by the producer can be set to a reasonable maximum to help bound the interactive solution

2. The Koval factor is greater than 1.

3. The Koval factor is set to a reasonable maximum number; 50 has been found acceptable, for example.

4. Pore volume drained can be bound by current oil production (from the data sheet). Where field conditions (or at least nearby conditions) are constant, bounding Vp by Np makes matching water cuts fast and robust. However, if field conditions have changed significantly, Koval's method is attempting to fit water cuts by estimating a drained volume that has evolved over time. The Koval method assumes monotonically increasing water cut; it can either match early time data or the later data, but not both.

Referring now to FIG. 6, a schematic block diagram of an example computing system 600 that can be, in some embodiments, used to implement a flow geometry generating system. More specifically, the computing system 600 can be used to generate flow geometry, and for example, execute the embodiment illustrated in FIG. 1. The computing system 600 includes a processor 606 communicatively connected to a memory 608 via a data bus 610. The processor 606 can be any of a variety of types of special-purpose or general-purpose programmable circuits capable of executing computer-readable instructions to perform various tasks, such as mathematical and communication tasks.

The memory 608 can include any of a variety of memory devices, such as using various types of computer-readable or computer storage media. A computer storage medium or computer-readable medium may be any medium that can contain or store the program for use by or in connection with the instruction execution system, apparatus, or device. By way of example, computer storage media may include dynamic random access memory (DRAM) or variants thereof, solid state memory, read-only memory (ROM), electrically-erasable programmable ROM, optical discs (e.g., CD-ROMs, DVDs, etc.) magnetic disks (e.g., hard disks, floppy disks, etc.), magnetic tapes, and other types of devices and/or articles of manufacture that store data. Computer storage media generally includes at least one or more tangible media or devices. Computer storage media can, in some embodiments, include embodiments including entirely non-transitory components. In the embodiment shown, the memory 608 stores a flow geometry generating system 612, which represents a computer-executable application that can implement the method 10 of FIG. 1 discussed in further detail hereinabove. The flow geometry generating system 614 can include a flow geometry engine 616 for generating the flow geometry.

However, those of ordinary skill in the art will appreciate that an “application” is not necessary for implementation, and instead, for example, the memory 608 may store computer instructions executable by the processor 606 to carry out the disclosed operations described in this disclosure. Both the processor 606 and the memory 608 can be physical items.

Returning to the memory 608, the memory 608 additionally includes a production related data memory 622 for storing the production related data 624 discussed herein. For example, the production related data 624 can include water cut data 626 that can be used with Koval, as well as tracer data 628 that can be used to constrain the flow geometry that is generated by the method 10 of FIG. 1. The memory 608 can also include algorithms and equations 630, including the following equation for minimizing the difference between a field Lorenz coefficient and a modeled Lorenz coefficient

$F = {^{\frac{1}{\alpha}{\lbrack{{\ln \; \Phi} + \frac{({1 - \Phi})}{\beta}}\rbrack}}.}$

The computing system 600 can also include a communication interface 602 configured to receive data streams (and transmit notifications, if applicable), as well as a display 604 for presenting the production related data 624, the flow geometry generated by the flow geometry generating system 612, items generated based on the generated flow geometry (e.g., qualitative information such as x percentage of flow from y percentage of pore volume of the reservoir under analysis and quantitative information such as slug size for conformance control and estimate of sweep vs time for the reservoir under analysis). The communication interface 602 and/or the display 604 may also be coupled to any number of input/output devices, for example, for receiving user input (e.g., expert data).

Alternatively, in some embodiments, a spreadsheet can be utilized.

Although the present disclosure and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the scope of the disclosure as defined by the appended claims. Moreover, the scope of the present disclosure is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present disclosure, processes, machines, manufacture, compositions of matter, means, methods or steps, presently existing or later to be developed that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present disclosure. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.

REFERENCES

All patents and publications mentioned in the specification are indicative of the levels of skill in the art to which the disclosure pertains. All patents and publications are herein incorporated by reference to the same extent as if each individual publication was specifically and individually indicated to be incorporated by reference.

Shook, G. M. “A Simple, Fast Method of Estimating Fractured Reservoir Geometry from Tracer Test,” Trans., Geothermal Resources Council, Vol. 27, September 2003.

Wu, X., Pope, G. A, Shook, G. M., and Srinivasan, S., 2008, “Prediction of Enthalpy Production from Fractured Geothermal Reservoirs using Partitioning Tracers,” International Journal of Heat and Mass Transfer, 51 (2008), 1453-466.

Shook, G. M. and Mitchell, K. M., “A Robust Measure of Heterogeneity for Ranking Earth Models: The F-PHI curve and Dynamic Lorenz Coefficient,” SPE 124625 presented at the 2009 SPE ANuual Technical Conference and Exhibition, New Orleans, La., October 4-7.

Shook, G. M., G. A. Pope and K. Asakawa, “Determining Reservoir Properties and Flood Performance from Tracer Test Analysis,” paper SPE 124614 presented at the 2009 SPE Annual Technical Conference and Exhibition, New Orleans, La., October 4-7.

Koval, “A method for predicting the performance of unstable miscible displacement in heterogeneous media.” SPE J3(2): 145154, 1963.

Sayarpour, M., 2008. Developments and Application of Capacitance-Resistive Models to Water/CO2 Floods, Ph.D. Dissertation, The University of Texas at Austin, Austin, Tex.

U.S. Pat. No. 8,428,924 U.S. Patent Publication No. 2013/0132052 U.S. Pat. No. 8,646,525 U.S. Patent Publication No. 2011/0320128 

1. A computer-implemented method for determining a flow geometry of a subsurface reservoir, the method comprising: (a) receiving production related data for the reservoir, wherein the reservoir is associated with a flooding operation; (b) generating a heterogeneity factor from the production related data; (c) calculating a flow geometry of displacement of hydrocarbons from the reservoir responsive to the heterogeneity factor; and (d) outputting the flow geometry.
 2. The method of claim 1, wherein the heterogeneity factor is at least one of a Koval factor, a Lorenz coefficient, or a Dykstra-Parsons coefficient.
 3. The method of claim 1, wherein the production related data is at least one of production rate of water, water cut, production rate of oil, production rate of gas, injection pressure, injection volume, temperature, natural tracers, artificial tracers, or tracer proxies.
 4. The method of claim 2, wherein the Koval factor is generated from the production related data that includes water cut data.
 5. The method of claim 4, wherein calculating the flow geometry further comprises converting the Koval factor to a Lorenz coefficient.
 6. The method of claim 5, wherein calculating the flow geometry further comprises minimizing an objective function, and wherein minimizing the objective function comprises minimizing a difference between a field Lorenz coefficient and a modeled Lorenz coefficient. $F = {^{\frac{1}{\alpha}{\lbrack{{\ln \; \Phi} + \frac{({1 - \Phi})}{\beta}}\rbrack}}.}$
 7. The method of claim 6, wherein Φ is less than 0.5.
 8. The method of claim 1, wherein data points in the production related data are weighted based on perceived error.
 9. The method of claim 1, wherein discrepancies in the production related data are removed from the production related data.
 10. The method of claim 1, further comprising optimizing operating parameters from the flow geometry.
 11. The method of claim 1, further comprising locating potential infill opportunities based at least in part on the flow geometry.
 12. The method of claim 1, further comprising optimizing sweep based at least in part on the flow geometry.
 13. The method of claim 1, further comprising optimizing size conformance treatment based at least in part on the flow geometry.
 14. The method of claim 1, wherein the flow geometry is a F-Φ curve.
 15. A system for determining a flow geometry of a subsurface reservoir, the system comprising: a processor; and a memory storing computer executable instructions that when executed by the processor cause the processor to: (a) receive production related data for the reservoir, wherein the reservoir is associated with a flooding operation; (b) generate a heterogeneity factor from the production related data; (c) calculate a flow geometry of displacement of hydrocarbons from the reservoir responsive to the heterogeneity factor; and (d) output the flow geometry.
 16. The system of claim 15, wherein the heterogeneity factor is at least one of a Koval factor, a Lorenz coefficient, or a Dykstra-Parsons coefficient.
 17. The system of claim 16, wherein the Koval factor is generated from the production related data that includes water cut data.
 18. The system of claim 17, wherein calculating the flow geometry further comprises converting the Koval factor to a Lorenz coefficient.
 19. The system of claim 18, wherein calculating the flow geometry further comprises minimizing an objective function, and wherein minimizing the objective function comprises minimizing a difference between a field Lorenz coefficient and a modeled Lorenz coefficient $F = {^{\frac{1}{\alpha}{\lbrack{{\ln \; \Phi} + \frac{({1 - \Phi})}{\beta}}\rbrack}}.}$
 20. A method for hydrocarbon production from a subterrancan reservoir, comprising flooding the subsurface reservoir in accordance with a flow geometry generated by the method of claim
 1. 